[S21P-08] Acquiring a Stochastic Differential Equation Representation to Characterize Tremors from Seismic Waveform Data Using Deep Learning
Non-volcanic low-frequency tremor has been observed in many subduction zones. These tremors are characterized by weak and intermittent seismic motion with dominant low-frequency (2-8 Hz) components and exceptionally long duration, often occurring in regions slightly deeper or shallower than typical megathrust earthquakes. Understanding tremors is significant for gaining insights into the mechanics of large earthquakes. However, due to their small amplitudes and continuous occurrence, it is challenging to directly capture the detailed characteristics of tremor waveforms. It is common to convert waveforms into root-mean-square (RMS) envelopes to capture their energy feature. In previous research, Ide (2008) modeled tremor waveforms using stochastic differential equations (SDEs), specifically considering its asperity as following an SDE. This suggests that the energy of tremors fluctuates probabilistically as described by SDEs. Inspired by this prior work, it is thought that the RMS envelope of tremors can also be modeled using SDEs, which consider the probabilistic fluctuations of tremor energy. To better understand the detailed features of tremors, we aim to develop a flexible, data-driven SDE model that uses neural networks for the drift and diffusion terms to represent the RMS envelope of tremor waveforms. Signature Kernel, known for capturing fine path properties effectively is used in learning. Our results demonstrate that the model trained with Signature Kernel-Based loss achieves a smaller error than existing models. Furthermore, we analyzed the obtained model, showing that the drift term captures the global behavior of tremors while the diffusion term captures the local behavior. Many properties observed in our model align with those of existing mathematical models. Our results indicate the significant potential of Signature Kernel-Based deep learning methods for modeling slow earthquakes.